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In a two-processor distributed computer network, prior research showed that a maximum flow algorithm can be used to find optimal program-module-to-processor assignments to maximize the performance of distributed programs. This paper examines the sequence of optimal assignments found as the load on one processor is held fixed and the load on the other is varied. For every program module M there exists a critical load factor fM such that when the load on the processor with variable load is below fM, M is assigned to that processor by an optimal assignment, and is otherwise assigned to the other processor. This characteristic opens the possibility of doing optimal dynamic assignments in real-time.